Class 8 Chapter 6: Algebraic Expressions

Class 8 Chapter 6: Algebraic Expressions

Important Concepts and Formulas on Algebraic Expressions

1.      A symbol that can take different values is called a variable.

2.      A symbol having a fixed numerical value is called a constant.

3.      We can form an algebraic expression involving variables and constants using basic operations (+, –, ×, ÷) to connect them. For example, 5xy – 8 is an algebraic expression involving the variables x, y and constants 5 and 8.

4.      The signs ‘+’ and ‘–’ separate the expression into various parts. These parts are called terms.

5.      When terms have the same variables and if the powers of the variables are same, then they are called like terms, else they are unlike terms.

6.      The numerical factor in a term is called its coefficient.

7.      An algebraic expression having exponents as non-negative integers is called a polynomial.

8.      Polynomials having one, two and three terms are called monomials, binomials and trinomials, respectively.

9.      The degree of a polynomial is the degree of term having the highest exponent (or sum of exponents). For example, the degree of 3x + 2x2y – 7 is 3 (therefore, the term 2x2y has degree as 2 + 1 = 3).

10. To add or subtract algebraic expressions, we add or subtract the like terms together but keep the unlike terms as such. For example, (5x + 2xy + 7z + y) + (–3y + x – 3xy) = (5x + x) + (2xy – 3xy) + (–3y + y) + (7z) = 6x + (–xy) + (–2y) + 7z or 6x –xy – 2y + 7z.

11. To find the product of two expressions, multiply each term of the first expression with each term of second expression.

12. If an equation is true for all values of the variable, it is called an identity.

13. Some of the identities are:

·        (a + b)2 = a2 + 2ab + b2
·        (a – b)2 = a2 – 2ab + b2
·        (a + b) (a – b) = a2 – b2
·        (x + a) (x + b) = x2 + (a + b)x + ab